Consider the quadrilateral ABCD shown in the figure below, with E, F, G, and H as the midpoints of sides AB, BC, CD, and AD respectively. The intersection points of the lines AF, BG, CH, and DE define shaded regions with areas S,
S_{1}, S_{2}, S_{3}, and S_{4} respectively.
Prove that S = S_{1} + S_{2} + S_{3} + S_{4}.
Problem 176
Quadrilateral maze,
Midpoints and intersecting,
Proof awaits within.
Sketch and Design Typography for Problem 176 with iPad Apps!
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